Russian forces have begun an assault on the town of Sudzha, the main population center in the Kursk region that was captured by Ukraine last year, a top Russian commander said on Tuesday. The advance puts Moscow on the verge of ending the first invasion of Russian territory since World War II.

Russia claimed Thursday that its troops have driven the Ukrainian army out of the biggest town in Russia’s Kursk border region, as a senior Kremlin official said that a U.S.-proposed 30-day ceasefire in the three-year war on Ukraine would help Kyiv by giving its military a break.

Russian forces have driven the Ukrainian army out of the biggest town in Russia’s Kursk border region, officials claimed Thursday, as U.S. officials sought the Kremlin’s response to a proposed 30-day ceasefire in the three-year war that Ukraine has endorsed.